MHB A family of functions where each member is its own inverse?

[eleventhxhour]

A family of functions is a set of functions that share one or more properties. ie: The family of quadratics with zeros 1 and 10, or the linear functions with a slope of 20.

there is a family of linear functions where each member is its own inverse. What linear property defines the family?

(I don't really know how to start this, though I think i understand what the question is asking. Help would be appreciated!)

 

[Evgeny.Makarov]

Any linear function can be written uniquely as $y=ax+b$ for some constants $a,b$. Find the inverse function $y=a'x+b'$ ($a'$ and $b'$ are expressed through $a$ and $b$). These functions are the same iff $a=a'$ and $b=b'$. The first of these equations will give you two possible values for $a$. Consider each value to see what constraint the second equation gives you on $b$.

A second way: The graph of the inverse function is obtained by reflecting the graph of the original function w.r.t. the line $y=x$. Find lines that are mapped into themselves by this reflection.